Influence of Indenter Tip Geometry on Elastic Deformation during Nanoindentation

Nanoindentation with a Berkovich indenter is commonly used to investigate the mechanical behavior of small volumes of materials. To date, most investigators have made the simplifying assumption that the tip is spherical. In reality, indenter tips are much more complex. Here, we develop a new method to describe the tip shape using the experimentally determined area function of the indenter at small depths (0–100 nm). Our analysis accurately predicts the elastic load-displacement curve and allows the theoretical strength of a material to be determined from pop-in data. Application of our new method to single crystal ${\mathrm{Cr}}_3\mathrm{Si}$ shows that the predicted theoretical strengths are within 12% of the ideal strength $G/2\pi$, where $G$ is the shear modulus.